506 The Tides in Relation to Geophysical and Cosmic Problems 



In investigating the tides of the solid earth, rj and >? are usually assumed 

 to be proportional to rj, as it is for the equilibrium tides, so that if 



r h = hrj , and r} = krj 

 7] = (1 — h-\- k)rj . 



y = (1 — h + k) then represents the ratio between the observed tidal range 

 forced by the tidal generating forces and the tidal range which would be 

 observed if the earth were completely rigid. 



It is not possible, in the case of semi-diurnal and diurnal tides to compute 

 the quantity y for a locality from a comparison between the amplitude of 

 a partial tide derived from the harmonic analysis and the amplitude derived 

 theoretically from the equilibrium theory assuming an absolutely rigid earth, 

 because these waves do not have a tidal development which corresponds 

 approximately to the equilibrium theory. For the long period tides, however 

 (especially the fortnightly and monthly partial tides) there is a probability 

 that they would have their full equilibrium values if the earth were absolutely 

 rigid. It is easy to compute these values; the difficulty is rather in obtaining 

 reliable observations for the semi-monthly and monthly partial tides. The 

 first comparisons of this kind which actually gave a proof of the tides of the 

 earth, were made by Thomson (Lord Kelvin, 1867) and Darwin (1883, 

 1911). Darwin used the harmonic constants of the semi-monthly lunar tide 

 observed on 33 stations and found y = 0-675, i.e. the observed tidal range is 

 approximately one-third smaller than the value computed from the equilib- 

 rium theory. Schweydar (1907) has analysed, using the same method, 194 

 annual observations, and he obtained essentially the same result: for the 

 semi-monthly lunar tides y = 0-6614, for the monthly lunar tide y = 0-6422. 

 The tides conformed to the theoretical times of high water, so that the as- 

 sumption of equilibrium tides appears to be justified. Later on it was possible 

 to produce a direct proof of the tides of the solid earth with a horizontal 

 pendulum. See for details Gutenberg (1929), Schmehl and Jung (1931) 

 and Hopfner (1936). However, there is a great spread in the derived values 

 for y, which has probably its origin in secondary phenomena mainly caused 

 by the pressure of the oceanic tides against the continents and by the at- 

 traction of the moving water-masses. According to Schweydar (1929), the 

 most plausible value for y = 0-841, whereas Prey (1929) holds that 0-74 is 

 the most probable value. Jeffreys (1929) gives 66 as the most reliable 

 value. It appears therefore that there is not yet sufficient certainty as to 

 the actual value of y. 



Proudman (1928) has proven that the hydrodynamical theory of the 

 tides, at least for narrow waters, like canals, is sufficiently developed to 

 permit the calculation of the tides of the solid earth. The restriction to narrow 



